A man standing on the horizontal ground observes that the building 50m away subtends an angle of 46 degree at his eye, which is 1.8 m above the horizontal ground. calculate the height of the building
Answers
The height of the building which is 50 m away from the man standing on the horizontal ground is 53.55 m.
Step-by-step explanation:
Referring to the figure attached below,
AB = the height of the man standing on the horizontal ground = 1.8 m
BC = the distance between the man and the building = 50 m
Angle of depression, θ = 46 ° = ∠EAD
Also from the figure, we can say that
AB // CD, AB = CD = 1.8 m
BC // AD, AD = BC = 50 cm
Now, consider the right triangle AED and applying the trigonometric ratios of the triangle, we get
tan θ = perpendicular/base
⇒ tan 46 = ED/AD
⇒ 1.035 = ED/50
⇒ ED = 51.75 m
Thus,
The height of the building is given by,
= ED + CD
= 51.75 + 1.8
= 53.55 m
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